Chapter 3

Use Euler diagrams to determine whether each argument is valid or invalid. All writers appreciate language. All poets are writers. Therefore, all poets appreciate language.

Use a truth table to determine whether the symbolic form of the argument is valid or invalid. \(p \rightarrow q\) \(\frac{\sim p}{\therefore \sim q}\)

Write the negation of each conditional statement. If I am in Los Angeles, then I am in California.

a. Use a truth table to show that \(\sim p \rightarrow q\) and \(p \vee q\) are equivalent. b. Use the result from part (a) to write a statement that is equivalent to If the United States does not energetically support the development of solar- powered cars, then it will suffer increasing atmospheric pollution.

Construct a truth table for the given statement. \(p \rightarrow \sim q\)

Let \(p\) and q represent the following statements: $$ \begin{aligned} &p: 4+6=10 \\ &q: 5 \times 8=80 \end{aligned} $$ Determine the truth value for each statement. \(\sim q\)

Let \(p\) and \(q\) represent the following simple statements: p: I'm leaving. a:You're staying. I'm leaving and you're staying.

Determine whether or not each sentence is a statement. René Descartes came up with the theory of analytic geometry by watching a fly walk across a ceiling.

Use Euler diagrams to determine whether each argument is valid or invalid. All physicists arc scientists. All scientists attended college. Therefore, all physicists attended college.

Use a truth table to determine whether the symbolic form of the argument is valid or invalid. \(p \rightarrow q\) \(\frac{\sim p}{\therefore q}\)

Write the negation of each conditional statement. If I am in Houston, then I am in Texas.

a. Use a truth table to show that \(p \rightarrow q\) and \(\sim p \vee q\) are equivalent. b. Use the result from part (a) to write a statement that is equivalent to If a number is even, then it is divisible by \(2 .\)

Construct a truth table for the given statement. \(\sim p \rightarrow q\)

Let \(p\) and q represent the following statements: $$ \begin{aligned} &p: 4+6=10 \\ &q: 5 \times 8=80 \end{aligned} $$ Determine the truth value for each statement. \(\sim p\)

Determine whether or not each sentence is a statement. The number of U.S. patients killed annually by medical errors is equivalent to four jumbo jets crashing each week.

Use Euler diagrams to determine whether each argument is valid or invalid. All clocks keep time accurately. All time-measuring devices keep time accurately. Therefore, all clocks are time-measuring devices.

Use a truth table to determine whether the symbolic form of the argument is valid or invalid. \(p \rightarrow \sim q\) \(\frac{q}{\therefore \sim p}\)

Write the negation of each conditional statement. If it is purple, then it is not a carrot.

Use a truth table to determine whether the two statements are equivalent. \(\sim p \rightarrow q, q \rightarrow \sim p\)

Construct a truth table for the given statement. \(\sim(q \rightarrow p)\)

Let \(p\) and q represent the following statements: $$ \begin{aligned} &p: 4+6=10 \\ &q: 5 \times 8=80 \end{aligned} $$ Determine the truth value for each statement. \(p \wedge q\)

Determine whether or not each sentence is a statement. On January 20, 2017, Hillary Clinton became America's 45 th president.

Use Euler diagrams to determine whether each argument is valid or invalid. All cowboys live on ranches. All cowherders live on ranches. Therefore, all cowboys are cowherders.

Use a truth table to determine whether the symbolic form of the argument is valid or invalid. \(\sim p \rightarrow q\) \(\frac{\sim q}{\therefore p}\)

Write the negation of each conditional statement. If the TV is playing, then I cannot concentrate.

Use a truth table to determine whether the two statements are equivalent. \(\sim p \rightarrow q, p \rightarrow \sim q\)

Construct a truth table for the given statement. \(\sim(p \rightarrow q)\)

Let \(p\) and q represent the following statements: $$ \begin{aligned} &p: 4+6=10 \\ &q: 5 \times 8=80 \end{aligned} $$ Determine the truth value for each statement. \(q \wedge p\)

Determine whether or not each sentence is a statement. On January 20,2017 , Donald Trump became America's first Hispanic president.

Use Euler diagrams to determine whether each argument is valid or invalid. All insects have six legs. No spiders have six legs. Therefore, no spiders are insects.

Use a truth table to determine whether the symbolic form of the argument is valid or invalid. \(p \wedge \sim q\) \(p\) \(\therefore \sim q\)

Write the negation of each conditional statement. If he doesn't, I will.

Use a truth table to determine whether the two statements are equivalent. \((p \rightarrow \sim q) \wedge(\sim q \rightarrow p), p \leftrightarrow \sim q\)

Construct a truth table for the given statement. \((p \wedge q) \rightarrow(p \vee q)\)

Let \(p\) and q represent the following statements: $$ \begin{aligned} &p: 4+6=10 \\ &q: 5 \times 8=80 \end{aligned} $$ Determine the truth value for each statement. \(\sim p \wedge q\)

Determine whether or not each sentence is a statement. Take the most interesting classes you can find.

Use Euler diagrams to determine whether each argument is valid or invalid. All humans are warm-blooded. No reptiles are warm-blooded. Therefore, no reptiles are human.

Use a truth table to determine whether the symbolic form of the argument is valid or invalid. \(\sim p \vee q\) \(\underline{\therefore q}\)

Write the negation of each conditional statement. If she says yes, he says no.

Use a truth table to determine whether the two statements are equivalent. \((\sim p \rightarrow q) \wedge(q \rightarrow \sim p), \sim p \leftrightarrow q\)

Construct a truth table for the given statement. \((p \vee q) \rightarrow(p \wedge q)\)

Let \(p\) and q represent the following statements: $$ \begin{aligned} &p: 4+6=10 \\ &q: 5 \times 8=80 \end{aligned} $$ Determine the truth value for each statement. \(p \wedge \sim q\)

Determine whether or not each sentence is a statement. Don't try to study on a Friday night in the dorms.

Use Euler diagrams to determine whether each argument is valid or invalid. All insects have six legs. No spiders are insects. Therefore, no spiders have six legs.

Use a truth table to determine whether the symbolic form of the argument is valid or invalid. \(p \rightarrow q\) \(q \rightarrow p\) \(\therefore p \wedge q\)

Write the negation of each conditional statement. If there is a blizzard, then all schools are closed.

Use a truth table to determine whether the two statements are equivalent. \((p \wedge q) \wedge r, p \wedge(q \wedge r)\)

Construct a truth table for the given statement. \((p \rightarrow q) \wedge \sim q\)

Let \(p\) and q represent the following statements: $$ \begin{aligned} &p: 4+6=10 \\ &q: 5 \times 8=80 \end{aligned} $$ Determine the truth value for each statement. \(\sim p \wedge \sim q\)

Let \(p\) and q represent the following simple statements: p: I study. \(q:\) I pass the course. Write each compound statement in symbolic form. I study or I pass the course.